University:
Bradley University
Course:
MTH 112 | Precalculus
Academic year:

2024
Views:

482

Pages:

6
Author:

segolhandworked

Honors Pre-Calculus MIDTERM REVIEW KrdXurtAj Name Miss Conflitti Use the graph to find the indicated function value. 6) y = f (x). Find f (-l ) ~ , 2, Use the graph to determine the x- and y-intercepts. 1) /K to- yr X - UTV l / s ^ V 7 7\ 4-3- \ \A -3 > + X f 5 - 4 /- 3 2 x 1 £ N a ' Give the domain and range of the relation.Determine . whether the relation is a function A/o -f q r ^n. cM CM Find and simplify the difference quotient f ( x + h) - f ( x ) > h* 0 for the given function. h ^ 2) {( 4, 4 ), (4, - 3), (- 8, - 6 ), (-12, 7), (1, -5 ) } D; ‘t , - g,- l -2- ) R: + , — 3 j - I -3 -4 w i 7) f (x) = X2 + 6 x + 8 Determine whether the equation defines y as a function of x. 3) + Evaluate the piecewise function at the given value of the independent variable. ) i 8) -I I 2 x - 5 if x < -5 f (x ) = 4x + 1 if x > -5 $ t-i -- *k- ) + 1 y=4 - Evaluate the function at the given value of the independent variable and simplify. 3> ( + I ) ~ *24) g(x) = 3x - 2; g(x + 1) x * 3x 1- 1 - 2. 3 +l - * Determine f ( 3). Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. Identify the intervals where the function is changing as requested. 5) /Is y 9) Increasing, Decreasing, and Constant V 4- 3 3 X xt 1 f ( XL -UI ) X -^ 2 \i/ - ( X^3 4> Xi- S\ 0^ 6 (S+ (eh 3 8 * 3 5 * -3 -2 3 ; x £ 2- * - 3 =4 - J . Inc. C-1 M 1 K bee (~ VxX> -3 ) e 1 fa i °°) Use the graph of the given function to find any relative Begin by graphing the standard absolute value function f (x) s= |x|. Then use transformations of this graph to graph the given function. maxima and relative minima. 10) f (x) = - 3x2 + \ M H> ^ 4 Begin by graphing the standard cubic function f (x) = x . Then use transformations of this graph to graph the given function. 13) g(x) = x3 2 ^ Begin by graphing the standard square root function f (x) = yfx . Then use transformations of this graph to graph the given function. 11) g(x) = “ - H - 1 - - Jx /K [W [ = 7» V £ 0 8 4 T. ct y m £ U x U s 3 K b 10 x 4 w \ >* • - Find the inverse of the one to-one function. 14) £(X ) = x- ^ 6 T 5 -x 2 V Find the vertex, axis of symmetry, x-intercepts, and y-intercepts to sketch the graph of the quadratic function. Determine the domain and range. 18) f (x) = x + 6x + 8 Does the graph represent a function that has an inverse function? 15) A y ^ A V: (.- hr 0 ^ Is OB' X r* -i H' 10 s) $0$) = - l f — V 1 TCr 0= - 0 r- CXVMUVV V ( -40, °°) £) — ^-) H x ' ( - 4 , 0') C- Z '0 ) ' ~ 'V Use the graph of f to draw the graph of its inverse 1 function. * ^~ 16) t / >4 U* ) V ^ Solve the problem. 19) You have 256 feet of fencing to enclose a rectangular region. What is the maximum area ? H h, o ) fe Ll i (o , ) ^ . ; CO , H ) / - > 4\ (V ‘ Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 20) f (x) = 9 x4 3X3+ 6x - 1; between 1 and 0 - 4 (- i > = >* Solve the problem. 17) An open box is made from a square piece of sheet metal 10 inches on a side by cutting identical squares from the comers and turning up the sides. Express the volume of the box, V, as a function of the length of the side of the square cut from each comer, x. *i J L. l* 1 0- V (xV z ( lO - l x. ) 10 6” 4“ ' - ii H H I I l l l I ll -12 -10 -8 -6 -4 -2 J. M zT -4 - - - 6 2S^ f -v Y 2 x -v 2 ~ 2SU 2 v - 7,S (o lz8 X -10 - - V = _ _ - us ( x ^ - lkx = 2(- l - /f ^« \ " x k GA - x (a* - n AcCA * I ^K <. IA -- -8" ^ ^ 5 ) * .- - X O ^ \ 2 4 6 X -3 * IT 1 x © f ((0o ), 0 )0 (§) ‘H - A MH-HH I I I I I I I t > ' • 10 2.x T3 - fries frjiJr o-x < 0 ^ X i -U + 5) y 8- - n* X ^ Aises Uf* © « A 10 - ^ y * X _u m= -i omplete the following: (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. (c) Find the y-intercept. (d) Find the maximum number of turning points (d) Graph the function. 21) f (x ) = x - 6x3 + 9x2 /K iz: s _ no J - ' Jf ( * > = 1 fUV 4 f ( I.? S .otzs )* - Determine the symmetry; find the y-intercepts; find the x-intercepts; find the vertical asymptotes; find the horizontal asymptotes; find the slant asymptotes, if any, plot at least one point between and beyond each x-intercepts and vertical asymptote; and graph the rational function. V4 -4x 22) f (x) = ..y ~ A/OKJL i 5 I - — 0 0 -z I I I Hit III ' = 5 10 ^ ) x ^ Koundyour 27) 3 - 0 . Z 22> 28) e 1-5 "int Use the compound interest formulas A = P 1 + Z (O/O ) and A Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval x = Pert to solve. 29) Find the accumulated value of an investment notation. 1 ) 0 ( ) < >) of $8000 at 9 % compounded continuously for 3 ) (xtf \ 4x2 x 4 > 0 years. $()O0 £ ® v S y \ 36 KW - — i ax +\ )U -Oio ! * - ^- i Soil If 30) Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years. Sooo (|4. • Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval JU - -2- 20 X4 H X - 2.X - 9 0 > notation. 24) 77I * 2 ll > O Write the equation in its equivalent exponential form. 31) logb 8 = 3 X +V - H4 -10-9 - 5‘7 -6 -5 . Write the equation in its equivalent logarithmic form. 32) 10* = 100 X I \ -- °5 loo = 4 -3 2 1 0 1 2 3 4 5 6 7 8 9 1 0 E* -^ Solve the problem. Evaluate the expression without using a calculator. 33) log2 8 T 25) The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 405 watts of power when 9 amperes of current is flowing through the resistor whose resistance is 5 ohms, find the power that a resistor needs to dissipate when 5 amperes of current are flowing through a resistor whose resistance is 7 ohms. P- 6 uX/f ( c Cu f ^e T ^^ ^ / H0 S - T5 K 1 34) log 5 125 35) log 7 1 36) log 3 ^ c :l ( 5x ) (l ) 37) 8 log 8 P P = 175 +K Uja - ^ - Approximate the number using a calculat answer to three decimal places. 0~*' _ ^ KuJ I 26) Body mass index, or BMI, takes both weight ( j ) z and height into account when assessing whether an individual is underweight or overweight. BMI varies directly as one's ) 7 weight, in pounds, and inversely as the square h of one's height, in inches. In adults, norma values for the BMI are between 20 and 25. person who weighs 182 pounds and is 72 inches tall has a BMI of 24.68. What is the BMI, * to the nearest tenth, for a person who weigh? * ' 'Jl N 128 pounds and who is 65 inches tall? T- 2- x --i x+4 £ - BAil 4 -* _ J—$ J~ X ^ J ~ X 7 - n -3 1 0 3^- 3 18 >O °°) 1) H , ' t >6° T Il -> C l , 00 ) +- > o T 3 1 I? ^ lb ^ 38 ) log 6 6 /3 Evaluate or simplify the expression without using a calculator. 39) In e4 H 40) In e l 41) In 1 o Find the domain of the logarithmic function. 42) f (x) = In (4 - x) *( < ^>, -x > -i -* Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 3, x4 *sjx + 5 43) loga 4 (x -2)2 - l . ^ —— 44) 3 logs 2 + ~r logs ( r 8J Solve the equation by expressing each side as a power of the same base and then equating exponents. ) 5(3« > 45) 9X + 8 = 27x - 5 3- S Vr 7* lo = 5s lojs 2- logs r 2 X 4- Uo = -JLKSI 5x Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 47) e x = 7 J^ e 5x = ^ XC ^ Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. :X 48) log (x2 - 8x) = 1 9 49) log 6 (5x - l ) = log 6 (2x + 8) w 1S 0 3 Solve the exponential equation. Express the solution set in terms of natural logarithms. ® =^X ^ =3 ^ 6r - - 21 logo 7 7 5x 'l = 2x + 5 *. Jx 3X ^ /IcTT *=^- H ( x- x 5 so = “? ] X * 2> Solve the problem. 50) Find out how long it takes a $2700 investment to double if it is invested at 8% compounded quarterly. Round to the nearest tenth of a year. Use the formula A = P 1 + 5ioo * a — n W/ t pvpo T7oo Solve. 51) The function A = A{)e”0 00866 x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 600 pounds of the material are placed in the vault, how much time will need to pass for only 212 pounds to remain? d A Ow (oOO - 2J2. le (oCO - -G - 0. OtoW k - K -t Ao , x O - 7/ ofc 3 LJK 7 X = 71° ^ juh ~no 0 Ao £ X / , o?\ Y -0* S' k ° y-fe S’ .f - 0 ^ oo » y 52 ) The half -life of silicon 32 is 710 years. If 30 grams is present now, how much will be present in 200 years? ( Round your answer to three decimal places. ) (6 j) A - Ae O' O g = - 0 .aortic, - 120 I 6 If A = Ao-^ oooWW 4 --

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